https://doi.org/10.1140/epjp/s13360-026-07301-8
Regular Article
Chain-type memristive maps featuring extreme multistability and their application in DCSK systems
1
Guizhou Key Laboratory of Artificial Intelligence and Brain-Inspired Computing, College of Mathematics and Big Data, Guizhou Education University, 550018, Guiyang, China
2
National Supercomputing Center in Changsha and College of Computer Science and Electronic Engineering in Hunan University, 410028, Changsha, China
3
School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore, Singapore
4
School of Mechanical and Electrical Engineering, Guizhou Normal University, 550025, Guiyang, China
5
School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, 210044, Nanjing, China
6
School of Artificial Intelligence, Guangzhou University, 510006, Guangzhou, China
a
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Received:
14
November
2025
Accepted:
7
January
2026
Published online:
21
January
2026
Abstract
The dynamic complexity of chaotic systems is crucial for secure communication, yet balancing this with structural simplicity and robustness remains challenging. To address this, we propose two novel hyperchaotic maps built by coupling multiple discrete memristors in chain-type architectures via direct cascade and parameter-controlled methods. Key steps involve designing memristor-based nonlinear units and interconnecting them into a feedback-rich chain structure with tailored coupling parameters. Dynamical analysis shows these maps exhibit initial-boosted extreme multistability and high complexity. The parameter-controlled design demonstrates strong robustness, maintaining a spectral entropy above 0.85 under perturbations. Both are physically realized on digital hardware. In differential chaos shift keying tests, they outperform recent chaotic maps and the Logistic map in bit error rate and security. This work provides a robust, implementable framework for enhancing secure communication with chaotic systems.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Qiao Wang and Zean Tian have contributed equally to this work.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
